Grating reflectors have been repeatedly discussed to improve the noise performance of metrological applications due to the reduction or absence of any coating material. So far, however, no quantitative estimate on the thermal noise of these reflectiv
e structures exists. In this work we present a theoretical calculation of a grating reflectors noise. We further apply it to a proposed 3rd generation gravitational wave detector. Depending on the grating geometry, the grating material and the temperature we obtain a thermal noise decrease by up to a factor of ten compared to conventional dielectric mirrors. Thus the use of grating reflectors can substantially improve the noise performance in metrological applications.
Reduction of coating thermal noise is a key issue in precise measurements with an optical interferometer. A good example of such a measurement device is a gravitational-wave detector, where each mirror is coated by a few tens of quarter-wavelength di
electric layers to achieve high reflectivity while the thermal-noise level increases with the number of layers. One way to realize the reduction of coating thermal noise, recently proposed by Khalili, is the mechanical separation of the first few layers from the rest so that a major part of the fluctuations contributes only little to the phase shift of the reflected light. Using an etalon, a Fabry-Perot optical resonator of a monolithic cavity, with a few coating layers on the front and significantly more on the back surface is a way to realize such a system without too much complexity, and in this paper we perform a thermal-noise analysis of an etalon using the Fluctuation-dissipation theorem with probes on both sides of a finite-size cylindrical mirror.
